On the covering radius of Simplex codes

Abstract

Lower and upper bounds for R(S k (q)) , the covering radius of a k -dimensional q -ary Simplex codes are determined. These help in getting bounds with a gap of one for S 3 (q) . Exact covering radius of S 2 (q) , S 3 (3) , S 4 (3) , S 4 (4) and S 3 (q) for q even are obtained.

A note on covering radius of MacDonald codes

“…Hence possible nonzero weights in are , · ½ , · ¾ , Ò ½ and Ò. By Lemma 4, ¼ for ½ ¾ ¿ The MacWilliams identities(5) gives…”

“…Many lower and upper bounds have been obtained [3], [4]. Very little is known about the covering radius of simplex codes [5] and almost nothing is known about the covering radius of MacDonald codes. The covering radius of an [n,1,n] repetition code is Ò Ò Õ [5].…”

“…Very little is known about the covering radius of simplex codes [5] and almost nothing is known about the covering radius of MacDonald codes. The covering radius of an [n,1,n] repetition code is Ò Ò Õ [5]. If ¼ and ½ are binary codes generated by the matrices ¼ and ½ respectively and if C is the code generated by the matrix…”